Marc Daniels
12th/11th grade Physics
Electric Fields and Potential Difference Unit Plan (3 to 4 days)
This unit follows the unit on electrostatics and builds on the idea of charges and electric
fields. It also introduces students to voltage or potential difference, which will be used
frequently in the next unit that focuses on electric circuits. Many of the initial ideas and
concepts, similar to the electrostatics unit, are abstract ideas, while some incorporate the
use of hands on labs and numerical equations.
Goals/Objectives:
 To introduce students into electric fields
 Have students use what they have learned about electric force and be able to
apply it to electric fields and potential difference.
 Students will be able to interpret and draw and interpret electric field lines
 Introduce students to concepts of conductors at electrostatic equilibrium
 In this unit, students will be introduced to voltage as well as capacitance
which play a large role in the application of creating and using circuits.
(learning concepts to be applied in hands on activities such as lab.)
Materials
Physics teacher edition text book
Other Physics books (for resources)
Van de Graff (for demonstration)
Materials for Lab (materials for Building a Radio speaker)
 Plastic cups
 Magnet wire
 Sand Paper
 Magnets
 Alligator clips
 Headphone Jacks
 Radio with batteries
 Pencils or Pens
 Scissors
 Speaker wire
 Tape
 Wire Cutters
 Lab instructions
Day 1
Introduction
Questions from Review Sheet
What are Electric Fields?
Electric fields are fields that permeate the space around a charged object and
another object experiences an electric force. (The fields around charged
objects that cause a force on other objects)
Electric Fields exist in the region of space around a charged object. When
another charged object enters this electric field, you get electric forces.
Let’s say that you have a small positive charge q0 that is placed near a
second charge that is larger and positive Q. The strength of the electric field
E, at the location of q0 is defined as the magnitude of the electric force acting
on q0 divided by the charge of q0
This is the electric field at the location of q0 produced by the charge of Q,
NOT THE FIELD PRODUCED BY q0. We sometimes call q0 a test charge.
Key Equation: E = F(electric)/ q (the units are in Newtons/Coulombs
The electric field is a vector quantity
Drawings of positive charges and negative charges and the direction of the
electric field done on the chalkboard (p. 643 of Holt)
Electric field line direction depends on the sign of the charge producing the
field. It depends on Q. Why? Show how the charges cancel out using algebra.
Fe=Kc Qq0/r^2
E= Fe/q0=Kc Qq0/ q0r^2
The q0 (test charge cancels out) So the Electric field is dependent on Q.
Electric field strength = Coulomb Constant x Charge producing the field/
(distance^2)
If Q is positive the field is directed outward away from q. If Q is negative, the
field is directed toward q.
(Electric Field Strength equations and examples to do in class)
Electric Field Lines
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This is a way to visualize the electric field lines. The lines do not
actually exist, but is a model we use to analyze fields. They represent
strength/magnitude as well as direction.
Electric field lines point away from positive charges, and into negative
charges (do drawing on the board)
The line charges begin on positive charges or at infinity and must
terminate on negative charges or infinity.
The number of lines drawn leaving a positive charge and approaching
a negative charge is proportional to the magnitude of the charge.
(draw and example with 2q and -q)
No two field lines can cross each other.
(draw two examples of unlike and like charges p. 649 of Holt Physics)
Electrical Potential Difference is derived and introduced, and example
problems are done during class.
Day 2 and Day 3 Potential Difference Revisions and Explanations
1. Apple Problem
Draw Electric Field Lines around a two equal but opposite charges. Indicate
the direction the field lines point.
Apple Problem
What is Electric filed intensity of a charge of 1.5 x 10 ^-6 C that experiences
an electric force of 4 x 10 ^-2 N? (Use equation E = F/q). What is the
electric field intensity if the charge is moved two times further away from the
field? (what happens when d is doubled? Use F = Kq1q2/d^2)
2. Review of Homework/ Example Problems (some recap and explanation)
p. 559 and 560, 52,55,57,60
p. 584 and 585, 43-48, 66-68
Ideas to Outline
Potential Difference General
V = W/q = Fd/q
 Electrical Potential Difference is dependent on
displacement field.
Potential Difference in a Uniform Field
V = Ed
 The electrical potential difference in an uniform field is
equal to the product of electric field intensity and the
distance moved by a charge
 The only reason we can make the V = Fd/q = Ed
transition is because F is uniform and constant
3. Potential Difference is revisited under different circumstances, such as when
a charge is in a uniform field.
Energy and Electric Potential (conceptual and mathematical)
 Recall the differences between gravitational potential energy
and kinetic energy
 There are similarities with electric fields moving charges
different distances from one another change the potential
energy
 We call this electric potential difference of dV.
 It is defined as the work done moving a positive test charge
between two points in an electric field divided by the
magnitude of the test charge.
 dV= W(on q)/q.
 Recall that W = Fd
 Electric potential is measured in joules per Coulomb (ask what
are the units of work and the units of charge) This gives you a
unit called a volt.
Do drawing of gravitational potential energy and Electric potential energy.
(page 569 of Teacher edition book. This serves as a visual representation of
the concept of potential energy)
When you move unlike charges apart you increase the potential difference.
So if you move unlike charges closer together the electric potential difference
reduces.
(Include drawing from p. 570 of teacher edition)
4. What is equipotential (conceptual, some math)?
 Lets suppose you move a test charge in a circle around a negative charge.
Here the distance between the test charge and the negative charge never
changes. So the potential difference is zero. The force that the electric
field exerts on the test charge is perpendicular to the direction that its
moved. So no work is done!!. Whenever Electric potential difference is
zero it is said to be at equipotential.
(Include drawing of negative charge and test charge in a circular orbit)
We can also measure differences in electric potential energy by dV= V2-V1.
Here we consider the change in energy from a test charges final and initial
position.
5. What happens to Electric Potential Difference when we have like charges!!!?
(ask first, thinking about the concepts when you have unlike charges)
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Recall that unlike or opposite charges attract one another.
Like charges repel from one another
When two like charges are brought closer together their potential
energy increases, because they “want to repel more”\
When they are further apart, their potential energy decreases because
the forces repelling them decreases
(Include drawing from p. 570 of teacher’s edition book)
6. Electric Potential in a Uniform field (mathematics and concepts)
 Now let’s talk about what happens when you have a uniform electric
field!!
 A simple uniform electric force and field can be made just by putting
two large, flat, conducting plates parallel to one another.
 One is positively charged, the other is negatively charged
 The electric field between the two is constant except on the edges of
the plates.
 The direction is from positive to negative
 Let’s say you put a positive test charge q’, and you move the charge a
distance d, that is in the opposite direction of the E field. Then you
have work being done……W = Fd. So dV = Fd/q’
 The electric field intensity is E = F/q’.
 (Do some algebra to get next equation)
 Now if we combine these equations we can get dV = Ed. (This is for
the electric potential difference in a Uniform Field ONLY!)
 Example Problem: # 3 on page 572 of teacher edition book
 Electric potential energy is higher at a positively charged plate,
because our test charge is positive.
 Example Problem: # 4 page 574 of teacher edition book. This will be
used to compare electric and gravitational force in a uniform field.
Aside: The Millikan Oil Drop Experiment
7. Charged Spheres (more conceptual than mathematical)
 Recall if you have two identical spheres, except one contains positive
charge, and the other is neutral.
 If you have the two spheres touch, the positive charge will be
distributed evenly between the two spheres. (but what if you have
different sized spheres?)
 In this case, let’s say you have a large sphere and a smaller sphere,
both with the same amount of charge in them. Because of the sizes of
the spheres the electrical potential difference is different in each
sphere.
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The larger sphere has a lower V, because the charges are able to
spread further apart and potential energy is lower (recall when like
charges are closer, potential is higher).
The smaller sphere has a higher V because the charges are closer
together.
What if we bring these two spheres into contact?
The charges will move so that there is no electrical potential
difference. So they will move in a manner where each sphere has the
same voltage.
What changes however, is that each sphere will contain different
amounts of charge.
With same size we get equal charge and voltage at contact. With
unequal spheres we get Same voltage but different charge at contact.
They are both going for the same electrical potential difference.
8. Different types of Conductors and Electric Fields Near Conductors
(Conductors in Electrostatic Equilibrium)
 Charge will spread apart as far as possible to make energy as low as
possible. What you get then is charges all over the surface of a
conductor.
 If it is solid charge will distribute evenly around the surface
 If it is a hollow sphere charge will distribute on the outer surface.
 If it is an irregular shape, charge will distribute closest at sharp points
 Electric field is zero inside a conductor.
 The Electric field is perpendicular to the surface of the conductor
 The shape of the conductor can affect the E field around the
conductor on the outside. Especially with irregular shaped
conductors.
 (include a diagram on page 576 of teacher edition book)
 Recall the Van de Graff. Can anyone tell me how a Van de Graff
works? (draw on board). If too much charge accumulates you can get
a spark in the air!! (page. 652 of Holt Physics book)
9. Capacitors
 What is a Capacitor??
 Energy can be stored in an Electric field
 Devices were created that could store large amounts of electric
charge. One example is the leyden jar used in lab.
 The devices were made smaller and now we call them capacitors.
 The ratio of charged stored to electrical difference or C = q/dV is
what we call Capacitance or C. It is measured in units call Farads, F.
(not to be confused with coulombs).
 Capacitors are made up of two conductors that are separated by an
insulator.
 The two conductors have opposite but equal charge.
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They are used in circuits to store charge.
Things such as tv’s and computer screens have capacitors. So it
becomes dangerous to open them up even when they are turned off,
because it is storing charge.
As charge increases, electrical potential difference also increases.
Example Problem: #5 p. 578 of teacher’ edition book. A review of
capacitance/ a plug and chug.
Day 3
Apple Problem
What is the Capacitance of a charge of 3.9 x 10^-8 C with an electric potential
difference of 6 x 10^-4 V?
Day 3 focuses on finishing up some of the topics from the previous day. Mostly
charged spheres will be covered, and students will be given the opportunity to ask
questions. The homework will also be reviewed in class.
Mini-lesson: One of the students asked a question that I stated that I would get back
today. Today I gave a mini lesson as to why field lines go outside of a positive charge
instead of into a positive charge. (mainly convention, because the model was
developed before the discovery on an electron).
Once the topics are covered, students will be given a review guide as well as a review
sheet that includes example problems.
Assessment
Assessment will be done in the form of asking questions, especially to the
students who are typically silent in class, doing in class problems, including
apple problems, as well as review and grading homework/ in class work.
There is no lab that is effective enough to correlate to this unit, so during lab
students will be introduced to concepts that will be discussed later in the
year. The lab incorporates concepts of electromagnetism, energy conversion,
and sound waves. Another lab will consist of using topics that will be
discussed in the next unit. It serves more as an introduction to more
complicated concepts. It focuses on voltage, resistance, and current (Ohm’s
Law). Students will be developing/creating their own circuit and will be
measuring current and voltage to determine resistance.
Key Ideas
 An electric field exists in the region around a charged object
 Electric field strength depends on the magnitude of the charge producing the
field and the distance between that charge and a point in the field
 The direction of the electric field vector, E, is the direction in which an
electric force would act on a positive test charge.
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Field lines are tangent to the electric field vector at any point, and the
number of lines is proportional to the magnitude of field strength
E = F/q’
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Electric Potential Difference is the change in potential energy per unit charge
in an electric field
∆V = Won q’/ q’ (units in Volts)
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The electric field between two parallel plates is uniform between the plates,
except near the edges. In a uniform field, the potential difference is related to
the field strength.
∆V = Ed (units in Volts)
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Robert Millikan’s experiments showed that charge could be quantized
Robert Millikan also showed that the negative charge carried by an electron
is 1.60 x 10-19 C
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Charges will move in a conductor until the electric potential is the same
everywhere on the conductor.
Grounding makes the potential difference between an object and Earth equal
to zero.
Grounding can prevent sparks resulting from a neutral object making
contact with objects that have built up charge on them.
Electric fields are the strongest near sharply pointed conductors.
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Capacitance is the ratio of the charge on an object to its electric potential
difference
C = q/∆V (units in Farads or C/V)
Capacitors are used to store charge.
Chapter 21 Homework Syllabus
Due Tuesday March 4th,
Due Wednesday March 5th, Chapter 20-21 Review Worksheet done in class
Due Thursday March 6th, None, Test Day
Grading “Build A Radio Speaker” Lab
50 points for participation and 10 points for each question (5 questions total) = 100
points total.
Missing Labs from Kevin, Rob, Vinny, and Mark V.
Name
Chapter 20 and 21 Test – Electrostatics and Electric Fields (100 points)
1. Compare and Contrast gravitational and electrostatic forces.
2. What are two methods that objects can be charged? Describe them.
3. a. What will happen when two positive charges are brought near one another?
b. What will happen when two negative charges are brought near one another?
c. What if one charge is negative and the other charge is positive?
a.
b.
c.
4. If the electrostatic force is negative, is the force attractive or repulsive? Please
Explain.
5. What happens to the electrostatic force when the distance between two charges
is doubled?
6. You have a charge of + 3 x 10-7 C and a charge of -4 x 10-6 C. They are 10.0m
apart. What is the electrostatic force between them? Is the force attractive or
repulsive?
7. A force of 7000 N acts on a charge of 3.5 x 10-2 C in a uniform field over a
distance of .05 m. What is the potential difference of this system? What is the
electric field strength?
8. Two identical charges repel one another with a force of 30 x 10-3 N. They are
15m apart. How much charge do they have? (what is the charge of each charge?)
9.
Three particles are placed on a straight line. The left particle has a charge of
+4.6 x 10-6 C, the middle particle has a charge of -2.3 x 10-6 C, and the right
particle has a charge of -2.3 x 10-6 C. The left particle is .12 m from the
middle particle, and the right particle is .24m from the middle particle. Find
the total force on the middle particle.
10.
How are the field lines drawn around a positive charge and a negative charge
that have equal magnitudes of charge? (please draw)
11.
A test charge of 4 x 10-6 C is in an electric field with a strength of 8 x 106 N/C.
What is the force it experiences?
12.
How much work is being done on a charge of 4 x 10-7 C when the potential
difference is 35 V?
13.
What is the capacitance of a sphere that has a charge of 5.7 x 10-9 C when it
has an electric potential difference of 10V?
14.
Why would a person be safe inside a hollow conducting sphere?
Multiple Choice Section
1. As an electric field becomes stronger the field lines should be drawn
a. thicker
b. thinner
c. closer together
d. farther apart
2. In a good insulator, electrons are usually
a. free to move around
b. free to move around after an impurity has been added
c. semi-free to move around
d. tightly bound in place
3. A Capacitor is
a. a device that stores charge
b. made up of two conductors separated by an insulator
c. a device that measures electric potential differences
d. both a and b.
4. How much energy is needed to move an electron through an electric potential
difference of 100 Volts?
a. 1.0 J
b. 100 J
c. 1.6 x 10-19 J
d. 1.6 x 10-17 J
5. The diagram represents two charges separated by a distance d.
Which change would produce the greatest increase in the electrical force between
the two charges?
a. doubling one charge only
b. doubling d only
c. doubling d and one charge only
d. doubling d and both charges
6. When an electroscope is charged, its leaves spread apart because
a. like charges repel
b. charges exert force on other charges over a distance
c. positive and negative charges spread over the metal surfaces
d. both a and b.
7. The electric potential difference is 40V, and a test charge has a charge of
1.3 x 10-2 C. What is the capacitance?
a. 3.25 x 10-4 F
b. 3.25 x 102 F
c. .16 F
d. 4.5 x 10-5 F
8. The diagram below shows the initial charge and position of three identical metal
spheres, X, Y, and Z.
All three spheres are simultaneously brought into contact with each other and then
returned to their original positions. Which statement best describes the charge of
the spheres after this procedure is completed?
a. All the spheres are neutral.
b. Each sphere has a net charge of +4 x 10-6 coulomb.
c. Each sphere retains the same charge that it had originally.
d. Sphere Y has a greater charge than spheres X or Z.
Answer Key
Short answer and equation work
4pts 1.
Answers may vary when comparing gravitation and electric forces.
4pts 2.
Induction – charge by bringing objects near
touching.
6pts 3.
a. repel
4pts 4.
The force is attractive because in order to get a negative force, one
charge must be positive and the other charge must be negative.
Opposite charges attract one another.
4pts 5.
It is ¼ the original force
5pts 6.
Attractive force of -1.0788 x 10-4 N.
6pts 7.
10,000V. 200,000 N/C or V/m
5pts 8.
2.7401 x 10-5 C
8pts 9.
7.43079 N total
4pts 10.
Lines go out from a positive charge to infinity or to a negative charge.
Lines go into a negative charge.
5pts 11.
(4 x 10-6 C)(8 x 106 N/C) = 32 N
4pts 12.
(35 V)(4 x 10-7 C) = 1.4 x 10-5 J
5pts 13.
5.7 x 10-10 F
4pts 14.
no electric fields are inside the conductor. The charges are on the
surface of the conductor, not inside.
b. repel
Conduction- charge by
c. attract
6.60515 N and .82564 N
C = q/V C = 5.7 x 10-9 C/ 100 V
Multiple Choice (all 4pts each).
1. c.
2. d.
3. d.
4. d.
5. a.
6. d.
7. a.
8. b.
Need pictures for 5 and 8
Key Equations
Electric Force: F = Kq1q2/d2 (units in Newtons)
Electric Field Intensity: E = F/q’ (units in N/C)
Electric Potential Difference: ∆V = Won q’/ q’ (units in Volts)
Electric Potential Difference in a Uniform Electric Field: ∆V = Ed (units in Volts)
Capacitance: C = q/∆V (units in Farads or C/V)
Review of Unit Plan